Finally, the stochastic degree sequence model (SDSM) takes \(\mathcal {B}^{\text{SDSM}}\)  to be all binary \(m \times n\)  matrices, but also gives a process for generating these matrices with different probabilities. Each \(\mathbf {B^*}\)  is generated by filling the cells \(B^*_{ik}\)  with a 0 or 1 depending on the outcome of an independent Bernoulli trial with probability \(p^*_{ik}\) . The distribution of the random variable \(P^*_{ij}\)  arising from \(\mathcal {B}^{\text{SDSM}}\)  is Poisson-binomial with parameters which can be computed using the \(p^*_{ik}\)  (see Supplementary Text S1.4).[1]}, [2]} There are many ways to choose \(p^*_{ik}\) , but in the studies below we choose \(p^*_{ik}\)  so that it approximates \(\Pr (B^*_{ik} = 1)\)  for \(\mathbf {B^*}~\in ~\mathcal {B}^{\text{FDSM}}\) , with the goal of ensuring that the expected agent and artifact degree sequences of \(\mathbf {B^*}~\in ~\mathcal {B}^{\text{SDSM}}\)  match those of \(\mathbf {B}\) . Adopting such a version of SDSM implies, for example, that in each possible world a given species may be found on many or few islands and a given island may be home to many or few species, but the average number of islands on which a given species lives in all possible worlds and the average number of species that live on an given island in all possible worlds matches these values the observed world. The SDSM has been used to extract the backbone of bipartite projections of, for example, legislators co-sponsoring bills, [3]}, [4]}, [5]} zebrafish (Danio rerio) sharing operational taxonomic units,[6]} countries sharing exports,[7]} and genes expressed in genesets.[8]}
